I am a software engineer and live in Dhaka in Bangladesh.
My office is 7km far from my home. I am planning to commute to my office by bicycle every working day.
Is this reasonable plan? This is my route
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When I decided to get back in biking around 2 years ago (After not being in a bike since I was a teen) this was around the same amount of distance I had to pedal. My bike was a Schwinn Ridge Al mountain frame with slick tires and during the first week I couldn't complete the commute for more than 2 days in a row. After the second week it became a lot easier and since then I commute by bike almost everywhere within 20Km. 7Km is quite a small distance but depending on your current fitness you may need to bike only 3 out of 7 days the first week (With resting in between). After that it will became really easy for you.
I checked your route using the Google Streetview and found there are a lot of bicycle taxis out there, which suggests these roads are plenty used by bikes and you should have no problem with traffic speed, but be very careful with the basic cycling safety measures. Sticking to the same traffic patterns should help to make things safe enough, but you may want to ask fellow cyclists for tips.
If you already own a bike, give it a try on any free day! That will let you have a better understanding of what will be required.
Assuming you're a healthy individual and the conditions aren't dangerous, distance wise that looks to be very doable. Cycling is always going to be better for your health than sitting doing nothing or riding a bus or car. I would recommend riding that route one day before your actual day of work so that you know exactly what to expect. Also things to consider are what do you take to work? Will you need a backpack or saddle bags of some sort? Things like that.
I also live in Dhaka, and I think the question is taking into consideration all the factors such as heat, humidity and crazy traffic. The average temperature this time of year is around 32 degrees celsius.
Take spare clothing and change when you reach work since you will be sweating a lot. Drink tons of water and also get a pair of sleeves to cover your hands from the sun. Last but not least, buy a pair of mudguards if you don't have them already, you never know when you hit a puddle here.
The route you have mentioned is also very dangerous with lots of buses and no cycling lanes, so make sure you wear a helmet.